Contrary to Mark Novakowski answer, which for some reason has been upvoted by many, yes, it is a valid and satisfiable request.
In fact the standard, as Wrikken pointed out, makes just such an example. In practice, Apache responds to such requests as expected (with a 206 code), and this is exactly what I use to implement progressive download, that is, only get the tail of a long log file which grows in real time with polling.